No, that's how you estimate something completely different - the age of the hydrogen atoms that make up the water.
I believe that the GP's point is something like this: It says "the water is older than the sun", but what it really means is "the hydrogen atoms in the water are older than the sun".
The subsequent paragraphs explain how they go from "age of hydrogen atoms" to "age of the water." If you want more detail than is in the article (which is understandable), then you'll have to refer to the published paper.
I believe that the GP's point is something like this: It says "the water is older than the sun", but what it really means is "the hydrogen atoms in the water are older than the sun".